hello to all

I have some issue of understanding this criteria... it says:

my question is why it is "uniformly" convergent ? I just can't see the fact why we have here uniformly convergent series...Let

be positive numerical sequence for which is worth that for almost every

and every

is satisfied that

then if series:

is convergent then series (of functions) :

is uniformly convergent on set A.

Thanks for any help